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A354545
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Expansion of e.g.f. exp(x)^( cos(x) + sin(x) ).
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1
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1, 1, 3, 4, 9, -24, -143, -902, -1631, 5176, 109841, 664302, 1479841, -16079764, -240229975, -1395162974, 126628545, 101950486736, 1118811398113, 4468008939542, -46600859353919, -1019505781080044, -7952038289388071, 10041106628453162
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OFFSET
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0,3
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LINKS
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FORMULA
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a(0) = 1; a(n) = Sum_{k=1..n} (-1)^floor((k-1)/2) * k * binomial(n-1,k-1) * a(n-k).
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PROG
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(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)^(cos(x)+sin(x))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (-1)^((j-1)\2)*j*binomial(i-1, j-1)*v[i-j+1])); v;
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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